Now, instead of the blower and draft inducer both stopping, the blower alone stops. The draft inducer continues to run. The Burners kick on, etc. Instead of 1-5, it's going 2-5 without the draft inducer ever stopping. Why? What should I do about it?

Maybe I'm asking the wrong question. Maybe I ought to be asking why my furnace isn't staying on long enough to raise the temperature 3 degrees. I think it's shutting off prematurely and immediately starting a new cycle.

I think it may be my thermostat failing. This morning, after waking and turning up the thermostat setting to 67, the furnace went through three cycles--of course, with the draft inducer never seeming to turn off. So, I went to the thermostat. It read a room temp of 68, meaning that it should have been waiting for the room to drop temp before kicking on the thermostat. I dropped the setting to 66. The inducer stopped. The room temp returned to the screen as 70.
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DavidJan 16 '13 at 13:49

What is the make and model of the furnace and thermostat? A thermostat is typically an over elaborate temperature switch, and usually doesn't have much to do with the furnaces operation other than telling it when to turn on. I would be more focused on the furnaces control board, since that's typically the brains of the operation.
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Tester101♦Jan 16 '13 at 14:11

The comment about the thermostat makes me wonder if the lower stage of a two stage furnace isn't working.
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BMitch♦Jan 16 '13 at 14:17

It's a Comfortmaker C9MPD100J14C. The thermostat is a Honeywell RTH230B.
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DavidJan 16 '13 at 18:26